Design of an asteroid belt in TikZ

Question

How can I construct an asteroid belt in TikZ? That is my question: I get everything right, but I do not know how to make the asteroid belt.

I have no code to add besides the preamble with TikZ package since I don't know where to start.

Answer 1

Quick and Dirty

Code

\documentclass[tikz]{standalone}
\usetikzlibrary{backgrounds}
\tikzset{
    random dot/.style args={#1*#2:#3}{random dot*={#1}*{#2}:{#3} and {#3}},
    random dot*/.style args={#1*#2:#3 and #4}{
        insert path={\foreach \throwaway in {1,...,#1} {(canvas polar cs: angle={#2+rnd}, x radius={#3+#3/.5cm*rand}, y radius={{#4+#4/.5cm*rand}}) circle[]}}}
}
\tikzset{every picture/.append style={show background rectangle,background rectangle/.style={fill=black}, radius=.4pt+.2pt*rand}}
\begin{document}
\tikz{
  \draw[gray] circle[radius=2cm];
  \foreach \angle in {0,...,360}
    \fill[white] [random dot=2*\angle:2cm];}

\tikz{
  \draw[gray] circle[radius=2cm];
  \foreach \angle in {0,...,360}
    \fill[white] [random dot=1*\angle:2cm];}

\tikz{
  \draw[gray] circle[x radius=2cm, y radius=1.5cm];
  \foreach \angle in {0,...,360}
    \fill[white] [random dot*=1*\angle:2cm and 1.5cm];}
\end{document}

Output

PGF-keys supported

Code

\documentclass[tikz,convert=false]{standalone}
\makeatletter
\pgfkeys{
    /tikz/belt/.is family,
    /tikz/belt,
    radius/.style={x radius={#1}, y radius={#1}},
    radius dot/.style={x radius dot={#1}, y radius dot={#1}},
    x radius/.initial=1cm,
    y radius/.initial=1cm,
    x radius dot/.initial=.4pt,
    y radius dot/.initial=.4pt,
    randomize/.initial=1,
    randomize dot/.initial=1,
    start angle/.initial=0,
    end angle/.initial=360,
    step angle/.initial=1,
    density/.initial=1,
    x ring size/.initial=.1cm,
    y ring size/.initial=.1cm,
    do/.style={
        insert path={
            \pgfextra\pgfmathsetmacro\tikz@belt@next@angle{\pgfkeysvalueof{/tikz/belt/start angle}+\pgfkeysvalueof{/tikz/belt/step angle}}\endpgfextra
            \foreach \tikz@belt@angle in {\pgfkeysvalueof{/tikz/belt/start angle},\tikz@belt@next@angle,...,\pgfkeysvalueof{/tikz/belt/end angle}} {
                \foreach \@tempa[evaluate=\qrr@tikz@belt@randA using \pgfkeysvalueof{/tikz/belt/randomize}*(2*rnd-1)*\pgfkeysvalueof{/tikz/belt/step angle},
                                 evaluate=\qrr@tikz@belt@randB using \pgfkeysvalueof{/tikz/belt/randomize}*(2*rnd-1),
                                 evaluate=\qrr@tikz@belt@randC using \pgfkeysvalueof{/tikz/belt/randomize}*(2*rnd-1),
                                 evaluate=\qrr@tikz@belt@randD using \pgfkeysvalueof{/tikz/belt/randomize dot}*(.5+rnd),
                                 evaluate=\qrr@tikz@belt@randE using \pgfkeysvalueof{/tikz/belt/randomize dot}*rnd*360,] in {1,...,\pgfkeysvalueof{/tikz/belt/density}} {
                    +(canvas polar cs:%
                        angle={\tikz@belt@angle+\qrr@tikz@belt@randA},
                        x radius={\pgfkeysvalueof{/tikz/belt/x radius}+\pgfkeysvalueof{/tikz/belt/x ring size}*\qrr@tikz@belt@randB},
                        y radius={\pgfkeysvalueof{/tikz/belt/y radius}+\pgfkeysvalueof{/tikz/belt/y ring size}*\qrr@tikz@belt@randC})
                        circle[rotate=\qrr@tikz@belt@randE, x radius={\pgfkeysvalueof{/tikz/belt/x radius dot}*\qrr@tikz@belt@randD}, y radius={\pgfkeysvalueof{/tikz/belt/y radius dot}*\qrr@tikz@belt@randD}]
                }
            }
        }
    }
}
\makeatother
\newcommand*{\debug}[1][]{%
\fill[even odd rule,gray!50,#1] circle[x radius=\pgfkeysvalueof{/tikz/belt/x radius}+\pgfkeysvalueof{/tikz/belt/x ring size},
                                      y radius=\pgfkeysvalueof{/tikz/belt/y radius}+\pgfkeysvalueof{/tikz/belt/y ring size}]
                               circle[x radius=\pgfkeysvalueof{/tikz/belt/x radius}-\pgfkeysvalueof{/tikz/belt/x ring size},
                                      y radius=\pgfkeysvalueof{/tikz/belt/y radius}-\pgfkeysvalueof{/tikz/belt/y ring size}];}
\begin{document}
\tikz[belt/x radius=2cm] {\debug[gray!25]\fill[gray] [belt/do];}
\tikz[belt/x radius=3cm, belt/x radius dot=.3pt, belt/x ring size=1cm] {\debug\fill[black] [belt/do];}
\tikz\fill[gray,belt/do];
\tikz[belt, step angle=5, density=5]\fill[gray,belt/do]; % Both belt/step angle and belt/density influence the density of the dots in anti-proportional ways. (density should be integer and greater 0).
\tikz[belt, start angle=30, end angle=160]\fill[belt/do]; % not a full circle
\end{document}

Output

(Compile yourself. Don’t want to blow up this answer.)

Answer 2

With TikZ

I don't know how random your asteroids have to be, so this is maybe not good enough. It uses the dots pattern, so the 'asteroids' are evenly distributed. The border of the belt is randomized with the random steps decoration.

\documentclass{standalone}
\usepackage{tikz}
\usetikzlibrary{patterns,decorations.pathmorphing}
\begin{document}
\begin{tikzpicture}[decoration={random steps,segment length=5pt}]
\draw [black!40] circle[radius=2.65cm];
\fill [pattern color=black,pattern=dots,even odd rule,decorate] circle[radius=2.5cm] circle[radius=2.8cm];
\end{tikzpicture}
\end{document}

With Metapost

The following examples uses the luamplib package, and must be compiled with lualatex.

White asteroids, varying size, on black background:

\documentclass{standalone}
\usepackage{luamplib}
\begin{document}
\begin{mplibcode}
beginfig(1);
r=2cm;
fill unitsquare scaled 4.8cm shifted (-1.2*r,-1.2*r) withcolor black;
for i=0 upto 720:
   pickup pencircle scaled uniformdeviate(1.5);
   drawdot (r*cosd(i) + 2*normaldeviate, r*sind(i) + 2*normaldeviate) withcolor white;
endfor;
endfig
\end{mplibcode}
\end{document}

\documentclass{standalone}
\usepackage{luamplib}
\begin{document}
\begin{mplibcode}
beginfig(1);
r=2cm;
pickup pencircle scaled 1pt;
for i=0 upto 360:
   drawdot (r*cosd(i) + 2*normaldeviate, r*sind(i) + 2*normaldeviate);
endfor;
endfig
\end{mplibcode}
\end{document}

Answer 3

Here is a simple solution via TikZ with random rotated ellipse for each asteroid.

The code (ten lines):

\documentclass[tikz]{standalone}
\begin{document}
\begin{tikzpicture}
  \fill[black] (-2,-2) rectangle (2,2);
  \foreach \aster in {1,...,1000}{
    \fill[white,rotate=360*rnd] (rnd*360:rnd*0.2+1.5) circle(rnd*0.01+0.005 and rnd*0.01+0.005);
  }
\end{tikzpicture}
\end{document}

Edit: Here is a variant to put all asteroids on an ellipse.

The code:

\documentclass[tikz]{standalone}
\begin{document}
\begin{tikzpicture}
  \fill[black] (-4,-4) rectangle (4,4);
  \foreach \aster in {1,...,1000}{
    \fill[white] (rnd*360:3 and 2.5) ++(rnd*360:rnd*.3)
    circle[x radius=rnd*.02+.01,y radius=rnd*.02+.01,rotate=rnd*360];
  }
\end{tikzpicture}
\end{document}

Second edit: with Sun and planets.

\documentclass[tikz]{standalone}
\begin{document}
\begin{tikzpicture}
  \fill[black] (-5.5,-5.5) rectangle (5.5,5.5);
  \fill[orange] circle(0.2)
  ++(0:.1) node[anchor=west,font=\footnotesize]{Sun};
  \foreach \name/\radius in {Mercury/0.387,Venus/0.723,Earth/1,Mars/1.524,Jupiter/5.202}{
    \draw[gray] circle(\radius);
    \pgfmathsetmacro\angle{360*rnd}
    \fill[white] (\angle:\radius) circle(.05)
    ++(0:.05) node[anchor=west,font=\footnotesize]{\name};
  }
  \foreach \aster in {1,...,3000}{
    \fill[white] (rnd*360:2.55) ++(rnd*360:rnd*.45)
    circle[x radius=rnd*.02+.01,y radius=rnd*.02+.01,rotate=rnd*360];
  }
\end{tikzpicture}
\end{document}

Answer 4

\documentclass[pstricks,border=12pt]{standalone}
\usepackage{multido}
\SpecialCoor\pstVerb{realtime srand}

\begin{document}
\begin{pspicture}(-2,-2)(2,2)
\psframe*(-2,-2)(2,2)
\psset{linecolor=white}
\multido{\rA=0.0+1.131}{1000}{\qdisk(!1.5 Rand 0.5 sub 3 div add \rA\space PtoC){!Rand 20 div}}%
\end{pspicture}
\end{document}

Answer 5

TikZ Decorations

When I saw this question I thought of using the tikz decoration methods to answer it. After several hours poring over Chapters 21 and 30 of the manual I figured out how to do it in a few lines.

\documentclass{standalone}
\usepackage{tikz}
\usetikzlibrary{decorations}
\usetikzlibrary{decorations.markings}
\usetikzlibrary{backgrounds}

\pgfkeys{
   /pgf/decoration/asteroids/.style={
      markings,
      mark=between positions 0 and 1 step \pgfdecorationsegmentlength with {
         \draw[each asteroid] (0pt,rand*\pgfdecorationsegmentamplitude) circle[
            radius=((1/\pgfdecorationsegmentaspect-\pgfdecorationsegmentaspect)*rnd+\pgfdecorationsegmentaspect)*
            \pgfmetadecorationsegmentamplitude
         ];
      },
      aspect=0.618,       % minimum aspect of asteroid (sort of)
      amplitude=5mm,      % maximum distance from asteroid to path
      meta-amplitude=1pt, % radius of each asteroid
      segment length=1pt, % separation along path between asteroids
   },
   /tikz/each asteroid/.style={draw}
}

\begin{document}
\begin{tikzpicture}[
   show background rectangle,
   background rectangle/.style={fill=black},
   each asteroid/.style={draw=none,fill=white},
   decoration={asteroids}
]
   \draw[gray,postaction=decorate] (0,0) circle [radius=4cm];
\end{tikzpicture}
\end{document}

The aspect key is used to define the eccentricity of each asteroid. If the aspect is a, then each radius (x and y) of the asteroid is set to be a random number between a and 1/a times the value of the meta-amplitude key. So the aspect could end up being as much as a^2.

The nice thing about this code is it can be customized for other asteroids along other paths:

\begin{tikzpicture}[
   each asteroid/.style={draw=red,fill=green,opacity=0.5},
   decoration={asteroids,
      meta-amplitude=5mm,
      segment length=1cm,
      aspect=1
   }
]
   \draw[postaction=decorate] (0,0) -- ++(4,0) -- ++(-4,4)--cycle;
\end{tikzpicture}

Answer 6

With PSTricks. I use randomly positioned ellipses with random axes and orientation.

\documentclass[pstricks,border=12pt]{standalone}

\pstVerb{realtime srand}

\begin{document}
\begin{pspicture}(-4,-4)(4,4)
\psframe*(-4,-4)(4,4)
\psset{linecolor=lightgray}
\psLoop{1000}{\psellipse*[rot=!rand 360 mod](!Rand 2 div 3 add rand 360 mod PtoC)(!Rand 30 div 0.02 add Rand 30 div 0.02 add)}
\end{pspicture}
\end{document}

Note that Rand no longer produces a random real number between 0 and 0.5 inclusive. Its definition had been tacitly changed. Now it produces a random real number between 0 and 1 inclusive. It is not documented, nor announced, but it is still fun!